Crystallization kinetics theory

See liquid, Newtonian glass amorphous solid liquid crystals kinetic theory. 

Table 43. Deviations of results from crystallization-kinetic theories from experiment for selected polymers...

J. Kemeny, J. Sestak Comparison of crystallization kinetic theories derived by isothermal and nonisothermal methods Thermochim. Acta 110(1987)113... 

Figure 7.3 Scheme of the conical zone in space and time drawn for 2D crystallization. From two spherulites nucleated at time r, only one, with a center at point P, that is, at distance r(r,t) from A can reach A at time t. Modified from Piorkowska, E., et al. Critical assessment of overall crystallization kinetics theories and predictions. Prog. Polym. ScL 2006,57,549-575. Copyright 2006, with kind permission from Elsevier. 

The underlying theoretical basis for the overall crystallization kinetics of polymers is found in the theory developed for metals and other monomers.(25-29) In monomeric systems the fraction of the liquid transformed to crystal varies from 0 to 1 over the time course of the crystallization. As was pointed out, the transformation in polymers is rarely, if ever, complete. This well-established experimental fact, and the reasons for this restraint, present a major problem that needs to be resolved in extending the crystallization kinetics theories from monomers to polymers. However, before discussing polymers, it is instructive to examine the theoretical base that has been established for monomers. 

Table 9.2. Deviation of experiment crystallization kinetic theories for...

Mention was made in Section XVIII-2E of programmed desorption this technique gives specific information about both the adsorption and the desorption of specific molecular states, at least when applied to single-crystal surfaces. The kinetic theory involved is essentially that used in Section XVI-3A. It will be recalled that the adsorption rate was there taken to be simply the rate at which molecules from the gas phase would strike a site area times the fraction of unoccupied sites. If the adsorption is activated, the fraction of molecules hitting and sticking that can proceed to a chemisorbed state is given by exp(-E /RT). The adsorption rate constant of Eq. XVII-13 becomes... 

We now apply the thermodynamic and kinetic theory of Chapters 5-8 to four problems making rain getting fine-grained castings growing crystals for semiconductors and making amorphous metals. 

V. N. Kusovkov, O. Kortluke, W. von Niessen. Kinetic oscillations in the catalytic CO oxidation on Pt single crystal surfaces Theory and simulation. J Chem Phys 705 5571-5580, 1998. 

Having discussed some equilibrium properties of a crystal, we now outline and contrast the bases of the growth theories which will be dealt with in more detail later. The theories may be broadly split into two categories equilibrium and kinetic. The former [36-42] explain some features of the lamellar thickness, however the intrinsic folding habit is not accounted for. Therefore, at best, the theory must be considered to be incomplete, and today is usually completely ignored. We give a brief summary of the approach and refer the interested reader to the original articles. The kinetic theories will be the topic of the remainder of the review. 

In conclusion, it seems more likely that the folds go into the crystal sequentially as it is being formed, rather than forming through equilibrium considerations — this idea is used as a basis for kinetic theories. 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

In the final section of this chapter, we shall attempt to give a brief rationalization of the regularities and peculiarities of the reactions of non-labile complexes which have been discussed in the previous sections. The theoretical framework in which the discussion will be conducted is that of molecular orbital theory (mot). The MOT is to be preferred to alternative approaches for it allows consideration of all of the semi-quantitative results of crystal field theory without sacrifice of interest in the bonding system in the complex. In this enterprise we note the apt remark d Kinetics is like medicine or linguistics, it is interesting, it js useful, but it is too early to expect to understand much of it . The electronic theory of reactivity remains in a fairly primitive state. However, theoretical considerations may not safely be ignored. They have proved a valuable stimulus to incisive experiment. 

Hikosaka presented a chain sliding diffusion theory and formulated the topological nature in nucleation theory [14,15]. We will define chain sliding diffusion as self-diffusion of a polymer chain molecule along its chain axis in some anisotropic potential field as seen within a nucleus, a crystal or the interface between the crystalline and the isotropic phases . The terminology of diffusion derives from the effect of chain sliding diffusion, which could be successfully formulated as a diffusion coefficient in our kinetic theory. 

Fig. 10 Schematic diagram for the explanation of spinodal decomposition due to the orientation fluctuation of stiff segments occurring in the induction period prior to crystallization [19]. On the basis of Doi s kinetic theory [24,25] Vexcl> excluded volume b, nearly equal to the diameter d of the rod or stiff segment L, rod length (9, angle between neighboring rods v, critical stiff segment concentration...

As described earlier, Doi s kinetic theory leads to a prediction that the SD is triggered by extension of unoriented crystalline sequences prior to crystal nucleation. In order to confirm this prediction the conformational change... 

Temperature programmed desorption (TPD) or thermal desorption spectroscopy (TDS), as it is also called, can be used on technical catalysts, but is particularly useful in surface science, where one studies the desorption of gases from single crystals and polycrystalline foils into vacuum [2]. Figure 2.9 shows a set of desorption spectra of CO from two rhodium surfaces [14]. Because TDS offers interesting opportunities to interpret desorption in terms of reaction kinetic theories, such as the transition state formalism, we will discuss TDS in somewhat more detail than would be justified from the point of view of practical catalyst characterization alone. 

Marsh B.D. (1988) Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization, I theory. Contrib. Mineral. Petrol. 99, 277-291. 

F. C. Frank, On the kinetic theory of crystal growth and dissolution process, in Growth and Perfection ofGrystals, eds. R. H. Doremus, B. W. Roberts, and V. Turnbull, New York, John Wiley Sons, 1958... 

The main observation from Table 2.1 is the enormous range of values of diffusion coefficients—from 10 1 to 10 30 cm2/s. Diffusion in gases is well understood and is treated in standard textbooks dealing with the kinetic theory of gases [24,25], Diffusion in metals and crystals is a topic of considerable interest to the semiconductor industry but not to membrane permeation. This book focuses principally on diffusion in liquids and polymers in which the diffusion coefficient can vary from about 10 5 to about 10-10 cm2/s. 

An extension of the kinetic theory on cases when a mechanical pressure interacts with kinetic processes inside solid volume and on interfaces has wide application interests. The elastic deformations in solid are presented from influence of external forces and from presence of internal defects of crystal structure point defects (vacancy, intersite atoms, complexes of atoms, etc.), extended defects (dislocations and inner interfaces in polycrystals), and three-dimensional defects (heterophases crystals, polycrystals). 

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